Ochi 



T 



£ 



_cs_ 



X ^__B 



Fig. 21 - Explanatory sketch of 

 distances a, b, x, etc. 



^_ (<^e) ~ cross spectrum between wave and vertical ship motion measured 

 at two different points, w and x, respectively, 



S = distance between points w and x. 



If this correction is included, the correlation coefficient between wave and 

 ship motion at points X becomes: 



/^wx 



f/l'-.^CWe) COS (a-e)dcoV + [/$_ (o.^) sin (a-^)dajj 



(A.8) 



where 



\^- (^J 



C_ (OJ^) 



Q_ (^J 



c_ (Wg) = energy density of cospectrum between wave and vertical ship 

 motion measured at two different points, w and x, 



Q_ (%) = energy density of quadrature spectrum between wave and vertical 

 ^^ ship motion measured at two different points w and x, 



cT(co^) = tan-1 Jq_ (^eVC- ('^e) 

 [ wx / wx 



$ (&j ) = energy density of auto- spectrum of wave measured at point w, 



WW ^ 



^xx(^e^ = energy density of auto-spectrum of vertical ship motion meas- 

 ured at point X, 



= co^S/g, 



co^ = encounter period with wave = o) + cv/g)co^, 

 00 = wave period, 

 V = ship speed. 



584 



